Differential taxes, implying implicit subsidies, must in general be accepted as a legitimate policy option of domestic policy in a decentralised economy. On the other hand, such subsidies may have non-negligible distorting effects on international trade. From a very narrow perspective, subsidies to some producers normally put them on an advantage compared to other producers, including foreign ones competing in the same markets. From this partial approach it looks as if removing subsidies would benefit foreign producers. It is plausible that this perspective is as important as general economic efficiency considerations when governments take action against infringements of international rules of state aid. What seems to be less noticed is the implication of the fact that when someone receives a subsidy there must be someone else paying. Often this is just intended to be a domestic producer-producer transfer. The closest alternative if the subsidy is removed is therefore a flat-rate system keeping tax revenues constant. It is far from clear that foreign producers have anything to gain from such a change. On the contrary, it may just as well mean they will be
losing since many of their contenders now face reduced after tax costs. From one perspective, it is the foreign firms that have been favoured by the domestic subsidy scheme since it offered protection from domestic firms paying for the transfer. We have referred to this situation as the ‘state aid paradox’.
The dispute over differentiated payroll tax rates between Norway and ESA is a case in point that has been used throughout this paper as an example where the state aid paradox may apply. Moreover, the decision by the EFTA Court in favour of ESA has left the Norwegian Government with no other choice than to find alternative instruments if the regional effects under the ESA regime are considered unacceptable. An interesting policy option that could easily be analysed within the present framework is infrastructure investments reducing transport costs. There are already several studies on this subject, but the specific questions arising in the present context are not answered.13 Within the model we have employed, we have seen that the effects on market shares for EU goods are conditional on transport costs.
By an appropriate allocation of infrastructure investments, the worst case scenario for the EU with falling market shares everywhere, may indeed come true.14
13 Martin and Rogers, 1995a and 1995b, and Kilkenny, 1997.
14 Could even infrastructure investments qualify as illegal state aid? As long as there is no harmonisation of public infrastructure investment criteria in the European Economic Area, we might think the answer would be
‘no’. But responding to a parliamentary question in 1967, the Commission suggested the answer could be ‘yes’
if the infrastructure were to the benefit of certain undertakings or the production of certain goods (Parliamentary Question 28/67 by M. Dehousse, Journal Officiel des Communautés Européennes 2311, 1967). However, so far it does not appear to be any European infrastructure projects that have been considered illegal state aid.
Appendix. Microeconomic foundations
A.1. Preferences
Consumers have identical preferences regardless of occupation and location of residence. Everybody supplies one unit of labour, receiving vj/tjA and wj/tjB depending on skills. Recall that the producer wage rate in sector A is vj and in the B sector wj, whereas tjA and tjB are the payroll tax factors. Individual expenditure systems for A skilled and B skilled are
Hence, preferences are quasi homothetic, i.e., the Engel curves are straight lines (but not through the origin),15 and consistent with (4.5) in the main text.
A.2. The economic base sector
The economic base sector in a specific region consists of a large number of firms with identical constant returns to scale technology. Aggregate output is determined by assuming that profits are zero due to free entry and exit.
Skipping indices for region in the rest of the appendix, the unit cost function for a firm is written
( )
ln c y/ =βwlnw+βqln ,q βw+βq 1. (A.2)
Here, w is the wage rate paid by producers, q is a price index of inputs from the non-basic sector, c/y is unit cost, and the Greek letters again parameters. The primal of (A.2) is
Cobb-Douglas, lny= −(βqlnβq+βwlnβw)+βwln +βqln . The price index, q, is defined by
where qk is the price paid for input k, and σ is the elasticity of substitution between any pair of inputs. Using (A.3), I assume a finite number of inputs so large that the integer constraint is not binding. Defining z as a quantity index of intermediates and zk as the quantity of input k, the primal of (A.3) is the CES function,
1 1
15 See Deaton and Muellbauer, 1980a, pp. 144-45.
This technology has several well known attractive properties: a) The cost function is separable in w and q, b) costs decrease when the number of inputs from the basic sector increases, and c) no input from the non-basic sector is essential. Property a) implies that the cost minimising firm may proceed in two steps: First, it may choose how much labour, l, and aggregate input, z, to use conditional on any output level, y. Second, conditional on the optimal level of z, it may choose how much to use of the different inputs from the non-basic sector, zk. Property b) means that increased specialisation in the non-basic sector rather than subdivision of labour within a single firm, raises productivity.16 Property c) implies that the degree of specialisation within any region is endogenous.
Applying Shephard’s lemma to the two steps, from (A.2) we obtain the cost shares for l and z, / larger βq is, the more important are intermediates for production costs in the basic sector and the stronger is the effect of increased specialisation in the non-basic sector.
From (A.3) we obtain sub cost shares / ( / )1
We may write (A.5) as − = for any k, including k=s. Differentiating logarithmically w.r.t.
q
(
lnzk σ lnqk−ln
s, we obtain the demand elasticity, ( ln )
16 This point has been emphasised in the regional context by Nicholas Kaldor (1970, p. 340):
“To explain why certain regions have become highly industrialised, while others have not we must introduce quite different kinds of considerations – what Myrdal (1957) called the principle of ‘circular and cumulative causation’. This is nothing else but the existence of increasing returns to scale – using that term in the broadest sense – in processing activities. These are not just the economies of large-scale production, commonly considered, but the cumulative advantages accruing from the growth of industry itself – the development of skill and know-how; the opportunities for easy communication of ideas and experience; the opportunity of ever-increasing differentiation of processes and of specialisation in human activities. As Allyn Young (1928) pointed out in a famous paper, Adam Smith’s principle of the
‘division of labour’ operates through the constant sub-division of industries, the emergence of new kinds of specialised firms, of steadily increasing differentiation – more than through the expansion in the size of the individual plant or the individual firm.”
When specialisation increases, the sub cost share for input s goes to zero and the demand elasticity is simply equal to the elasticity of substitution.
A.3. The non-basic sector
The non-basic sector, the A sector, is also assumed to consist of firms with identical technology, but this time increasing returns to scale internal to the firms because of set up costs. The cost function for firm k is written,
1 0
k ( k
b = zς ς+ )v (A.7)
Here, bk is total costs and v is the producer wage rate prevailing in the non-basic sector. The primal to (A.7) is
( 0)
k k
z = m −ς /ς1, where mk is labour input. Marginal cost is ς1vand the set up cost isς0v. With internal economies of scale, there must be some kind of imperfect competition to obtain market equilibrium. Following most of the literature in the new economic geography tradition, let us assume that market structure is
monopolistic competition. The first order condition for profit maximising is
(1 1/ ) 1
k k
q − ε =ςv. (A.8)
Assuming specialisation is sufficient to substitute σ for εk (cf. eq. (A.6)), the profit maximising price for each differentiated product is equal to a constant mark up over marginal cost,
1 1
qk σ ςv
=σ
− . (A.9)
Monopolistic competition implies that profits vanish in equilibrium,
k k k 0
q z −b = . (A.10)
Since there are no profits, only labour input and intermediates are non-tradable, we note that the cost of intermediates for the basic sector is equal to the wage bill for the non-basic sector, qz vm= . By (A.4),
/ q /
vm β =wl βw (A.11)
as claimed in the main text.
Substituting for qk from (A.9) and bk from (A.7), we obtain the equilibrium output,
0( 1) /
m=ς σ0 n (A.14) where n is the number of firms. Since B sector productivity rises when the number of intermediate inputs rise and there is internal economies of scale, the number of firms is also equal to the number of products since it is not profitable for two firms to produce the same product. Using (A.9) and (A.14), we may rewrite (A.3) logarithmically as
In order to simplify, different normalisations are suggested in the literature. We could, e.g., set ς0and ς1 in such a way that ς1≡1/ς0− ≡ −1 σ 1, and write
, 1/ ,
k k k
q =σv z = σ m =1 (A.16)
This means that we can use m for the number of intermediate inputs. Although this kind of normalisations may prove useful for specific purposes, we should be aware that a change in σ implies an automatic change in the cost parameters and is probably best to avoid when comparative statics and numerical simulation is carried out.17
A.4. Mill prices
With free entry, mill prices are just sufficient to cover unit production costs in equilibrium,
lnp=βwlnw+βqlnq (A.17)
Substituting for ln from (A.15), using (A.11), we may express the mill price as a function of the B sector producer wage rate and labour inputs,
17 See Neary (2001), p.549, for other critical remarks on the use of normalisations in the new economic geography literature
A.5. Equilibrium with Cobb-Douglas preferences
Let us first consider market clearing based on aggregate demand systems consistent with individual Cobb-Douglas preferences and homogeneous consumers in the sense that everybody is using the same expenditure share on imports from either source, say αF, and the same share on home mades, αH. For adding up to hold, this means that αH = −1 2αF. It is reasonable to assume that expenditures on home mades at least match expenditures on imports from either other source, so we restrict the discussion to αH ≥αF. When adding up holds, this means that α ≤F 1/3.
In order to simplify, we will throughout assume symmetrical transport costs, τij =τji,that transport costs between region s and the two other regions are equal and smaller than between n and u,τL ≡τnu >τsu=τns≡τS,
Equation (A.20) and (A.21) are the market clearing conditions for products made in region n and s,
corresponding to (4.1) in the main text. (A.22) corresponds to (4.2), the restriction that tax revenues should be
kept constant. (A.23) and (A.24) are the mobility equilibrium conditions, corresponding to (4.9) and (4.10) (to go from (4.9) to (A.23), use (A.11)). Equation (A.25) is obtained by plain substitution.
Under the Norwegian regime we have that tnA=tnB=tn and the policy instrument, , is used to obtain a desired level for employment in the basic sector in the periphery, say the symmetric distribution
tn
n s / 2
l = =l l . Then, for (A.23) and (A.24) to hold, employment in the nonbasic sector must be given by mn =ms =m/ 2, and total population equally distributed, so we do indeed have a symmetrical outcome. With symmetry imposed, (A.23) is identical to (A.24), so we may ignore (A.23). Substituting from (A.25) in (A.24), the system is reduced to 4 equations. Furthermore, we may use (A.20) and (A.21) to obtain,
( ) ( ) that if there is no locational disadvantage for the periphery (τ=1), wage rates are equal and laissez-faire prevails regardless of expenditure shares (w wn/ s = =tn ts 1
1
= ) which of course is what we would expect from an intuitive point of view. When there is a disadvantage (τ< ), we notice that if we move towards autarky (αF →0
n = =s
), the right side of (A.26) becomes equal to the right side of (A.27) whereas the left sides take on different signs. Hence, the only possibility is that both sides equal zero, which is true when there is no taxation (t t ). Then, the regional wage rates are independent ( can take any value). If we move towards more openness, eventually with equal shares on home mades and imports (
1 wn/ws
This is a very special case, however, since it implies that the relative price level given by (A.25) is equal to (1/ )τ αFwhatever the distribution of employment is and whatever the relative wage rate is. Since changes in industry structure would have to work on the core-periphery structure through the relative price level, and the relative price level here is independent of industry structure, there is no endogeneous core-periphery mechanism and we could have done without the vertical industry structure since it does not add anything interesting to the model. However, this is very different when we consider intermediate cases between autarky and maximum openness. This is an equation of degree 2n-m. When m is less than n, the equation must be of degree 3 or more. With
and , corresponding to
αF = , we have a quartic equation. As shown by Abel in 1823, there is no algorithm for solving general algebraic equations of degrees higher than four, using radicals and arithmetic operations. Hence, it is possible to find the solution to the system for αF =1/ 6 and αF =2 / 9, but not the general solution for any permitted value of αF.18 We are therefore content to look at the two cases and study the qualitative behaviour of the system.
For αF =1/ 6, equation (A.29) can be written
Defining x t= −n 3 / 4the equation can be transformed into the simpler equation
( )
3 3 1/ 3 1 1 1/ 3 0
16 32
x − τ x+ +τ = .
18 This is strictly speaking incorrect, since Abel’s non-existence result only pertains to algorithms based on radicals and elementary arithmetic operations. For solutions of algebraic equations of higher degrees using modular functions, the reader is referred to King (1996).
The discriminant of the equation is positive, so we know there is one real root (and two complex roots).19
ing the quartic equation into a cubic, the Cardano form
e to compare graphic
Transform ula can again be used to obtain
It may be instructiv ally the solutions for with (tn αF =1/ 6and αF =2 / 9) and without (αF =1/ 3) the endogeneous core-periphery mechanism. The solutions are plotted in Figure A.1.
tn=1
Figure A.1. Regional subsidies compensating for locational disadvantage.
Note: The payroll tax rate in the north along the vertical axis and the locational disadvantage parameter, , along the horizontal axis.
The more open the economy is (αF large), the larger the necessary subsidy (small t ) has to be in order to maintain the symmetric population equilibrium. The figure also suggests that the curvature, reflecting the elasticity of substitution between subsidies and disadvantage, is more pronounced the more closed he economy
n
19 See Sydsæther (1981), p.54.
is. Hence, it appears to be relatively more demanding in terms of transfers to compensate a deterioration in relative transport costs, the more closed the economy is.
In principle, we could now proceed by solving for the other endogeneous variables. However, it is clear that the algebra at best would be messy, possibly without providing interpretable results. This lead based on closed form solutions is therefore left for future research. Here, we continue based on numerical methods that also allows for more general preferences.
A.5. Equilibrium
Without mobility, it is straightforward to solve the model as suggested in the main text. The aggregate income equations for region n and s, are
1
(
Solving for aggregate income in n, we get
(1 )( 1) ss ( 1) 1ns su u 1 ns
( ) (
The solution for aggregate income in s is even longer on terms and therefore left out.
The illustration and the numerical computations used in the main text are based on the following set of
numerical values: set γ ≡1/10and let γii≡γ and γij ≡ −γ/ 2 for all i,j. Set βw =βq and all αij equal, i.e. all
and the solutions conditional on tn
(32n1)
For the computation of real income, set σ ≡2 and use the normalisations (A.16). Also, assume symmetrical transport costs, τij =τji,assume that τL≡τnu >τsu =τns≡τS, and ignore domestic distribution costs, τii =1. Set
L 3/ 2
τ ≡ and τS ≡5 / 4 which means that transport costs between u and n equal half the price f.o.b. while the transport costs to and from region s equal a quarter.
We may express (A.20) and (A.21) using the producer wage rates, rather than aggregate income. Since
n n
in (A.20) and (A.21), we obtain the wage equations, illustrated in Figure 1 in the main text,
(
n 2)
( )(
References
Armington, P.S.,1969. A theory of demand for products distinguished by place of production, International Monetary Fund Staff Papers 16, 159-78.
Bairam, E.I.,1997. Levels of economic development and appropriate specification of the Harrod foreign-trade multiplier, Journal of Post Keynesian Economics 19, 337-85.
Baldwin, R., 2001. Core-Periphery model with forward-looking expectations, Regional Science and Urban Economics 31, 21-49.
Deaton, A. and Muellbauer, J.,1980. Economics and Consumer Behavior. Cambridge University Press, Cambridge.
Fujita, M., P. Krugman and Venables, A.J.,1999. The Spatial Economy: Cities, Regions and International Trade.
MIT Press, Cambridge Mass.
Hamermesh, D.S., 1993. Labour Demand. Princeton University Press, Princeton N.J.
Hamilton, S. F., 1999. Tax incidence under oligopoly: a comparison of policy approaches, Journal of Public Economics 71, 233-45.
Hervik, A.,1997. Benefits from reduced payroll taxes in Norway. Research report no. 8/1997, Norwegian School of Management, BI.
Kaldor, N., 1970. The case for regional policies, Scottish Journal of Political Economy 17, 337-348.
Kilkenny, M., 1998. Transport costs and rural development, Journal of Regional Science 38, 293-312.
King, R. B., 1996. Beyond the Quartic Equation . Birkhäuser, Boston.
Martin, P. and Rogers, C. A., 1995a. Industrial location and public infrastructure, Journal of International Economics 39, 335-351.
Martin, P. and Rogers, C. A., 1995b. Trade effects of regional aid, in: Baldwin, R., P. Haaparanta and Kiander, J. (Eds.). Expanding membership of the European Union. Cambridge University Press, Cambridge, pp.166-88.
Myrdal, G., 1957. Economic Theory and Underdeveloped Regions. Ducksworth, London.
Neary, J.P., 2001. Of hype and hyperbolas: introducing the new economic geography, Journal of Economic Literature XXXIX, 536-561.
Schina, D.,1987. State Aids Under the EEC Treaty Articles 92 to 94. ESC Publishing LTD, Oxford.
Shields, G.M. and Shields, M.P., 1989. The emergence of migration theory and a suggested new direction, Journal of Economic Surveys 3, 277-304.
Skott, P. and Roos, J., 1997. The “big push” in an open economy with nontradable inputs, Journal of Post Keynesian Economics 20, 149-62.
Sydsæter, K., 1981. Topics in Mathematical Analysis for Economists. Academic Press, London.
Venables, A. J.,1996. Equilibrium locations of vertically linked industries, International Economic Review 37, 341-59.
Vickerman, R., K. Spiekerman and Wegener, M., 1999. Accessibility and economic development in Europe, Regional Studies 33, 1-15.
Young, A. (1928), Increasing returns and economic progress, Economic Journal 38: 527-42.
Legal and public documents
Brussels: Study Programme on European Spatial Planning, 2000, Final Report (http://www.nordregio.se/) Brussels: EFTA Court, 1999, Judgement in Case E-6/98 (http://www.efta.int/structure/main/index.html) Brussels: EFTA Surveillance Authority, 1998, Decision No. 165/98/COL.
Brussels: Commission of the European Communities, 1998, Observations in Case E-6/98.
Brussels: Journal Officiel des Communautés Européennes 2311, 1967 Oslo: Act of 17 June 1966, No. 12.
Oslo: Ot. Prp. No. 12, 1974-75.
Oslo: Prp. No. 100, 1991-92.
Oslo: Government of Norway, 1998, Application for annulment to the EFTA Court.